Subtracting Multi-Digit Numbers

Check every column before you start. Any of them might be short.

Unbundling can chain

To subtract from 5,003 you may need to break a thousand, then a hundred, then a ten.

The number never changes

5,003 becomes 4 thousands, 9 hundreds, 9 tens and 13 ones. Still 5,003.

Check by adding

Add your answer to what you took away. It should return the number you started with.

Unbundling, several columns at once

When a column has too little to subtract from, open one unit from the column to its left: a thousand becomes ten hundreds, a hundred becomes ten tens. The value of the number is unchanged — only its packaging. This is the whole of multi-digit subtraction.

Unbundling across zeros

In 5,003 - 2,478 the tens and hundreds are both empty, so you must go left to the thousands and cascade: 5,003 becomes 4 thousands, 9 hundreds, 9 tens and 13 ones. Do the whole cascade first, writing every change down, and only then start subtracting.

Check by adding back

If 5,003 - 2,478 = 2,525, then 2,525 + 2,478 should return 5,003. It does. This check uses a different operation, so it is genuinely independent of the work you just did — unlike re-reading your own subtraction, which tends to repeat the same mistake.

When counting up is easier

For 5,003 - 4,987 the numbers are close, so counting up beats unbundling: 4,987 to 5,000 is 13, then 3 more is 16. Recognising when the algorithm is the wrong tool is part of being genuinely fluent rather than merely trained.